If you make separate components for the outer and middle shelves, you can use tags to control the visibility of these edges. But still don’t understand why don’t you combine the overlapping pieces into one?
If it was me I would copy the geometry, tag it and turn off the tag. Paste in place, fix the non solid component then use outershell to remove all the joins.
If the client needs it changed delete it and turn on the other tag and work on it, repeat as necessary.
I would also look into the correct use of Tags, yours are not right.
Tags is the new name for Layers, you have many layers in your model but as I’m opening it in 2022 they show as Tags. There is no difference except the name. Oh and now you can have Tag Folders.
You can read about how they should be used here.